Having more than one AV or Firewall installed on your computer is bad, it will slow down the computer, cause internet connection problems and leave you with no AV protection at all if they cancel each other out as they fight for resources.
Some info courtesy of admin here
Is the computer a brand name such as Dell or HP etc, if yes, these type of computers ship with all sorts of bloatware such as trial versions of AV and if such a trial AV was already running on the computer it would go some way to explaining why the Windows Firewall may have not been working, also worth mentioning is that many AVs cannot simply be removed in the Control Panel as they need to be properly uninstalled using a program provided by the AV vendor.